Answer
Yes, this is a right triangle.
Work Step by Step
The distance between A and B:
$$\sqrt{(-6-0)^2+(-4-(-2))^2}$$
$$\sqrt{36+4}$$
$$\sqrt{40}$$
The distance between B and C:
$$\sqrt{(0-(-10))^2+(-2-8)^2}$$
$$\sqrt{100+100}$$
$$\sqrt{200}$$
The distance between C and D:
$$\sqrt{(-6-(-10))^2+(-4-8)^2}$$
$$\sqrt{16+144}$$
$$\sqrt{160}$$
Now, check that these three points form a right triangle using the Pythagorean Theorem.
$$160+40=200$$
$$200=200$$
Yes, this is a right triangle.